Criteria for a successful theory of punishment include first, that it specify a reasonable limit to punishments in particular cases, and second, that it allow benefits to outweigh costs in a penal institution.It is argued that traditional utilitarian and retributive theories fail to satisfy both criteria, and that they cannot be coherently combined so as to do so. Retributivism specifies a reasonable limit in its demand that punishment equal crime, but this limit fails to allow benefits to outweigh costs of punishing. Utilitarians demand the latter but cannot guarantee the former. Combinations continue to violate one requirement or the other.